information.criteria {plsdof} | R Documentation |
Information criteria
Description
This function computes the optimal model parameters using three different model selection criteria (aic, bic, gmdl).
Usage
information.criteria(RSS, DoF, yhat = NULL, sigmahat, n, criterion = "bic")
Arguments
RSS |
vector of residual sum of squares. |
DoF |
vector of Degrees of Freedom. The length of |
yhat |
vector of squared norm of yhat. The length of |
sigmahat |
Estimated model error. The length of |
n |
number of observations. |
criterion |
one of the options "aic", "bic" and "gmdl". |
Details
The Akaike information criterion (aic) is defined as
{aic}=
\frac{{RSS}}{n} + 2\frac{{DoF}}{n} \sigma^ 2\,.
The Bayesian information criterion (bic) is defined as
{bic}= \frac{{RSS}}{n} +
log(n)\frac{{DoF}}{n} \sigma^ 2\,.
The generalized minimum description length (gmdl) is defined as
gmdl=\frac{n}{2}log(S)+\frac{DoF}{2}log(F)+\frac{1}{2}log(n)
with
S=\hat \sigma ^2
Note that it is also possible to use the function
information.criteria
for other regression methods than Partial Least
Squares.
Value
DoF |
degrees of freedom |
score |
vector of the model selection criterion |
par |
index of the first local minimum of
|
Author(s)
Nicole Kraemer, Mikio Braun
References
Akaikie, H. (1973) "Information Theory and an Extension of the Maximum Likelihood Principle". Second International Symposium on Information Theory, 267 - 281.
Hansen, M., Yu, B. (2001). "Model Selection and Minimum Descripion Length Principle". Journal of the American Statistical Association, 96, 746 - 774
Kraemer, N., Sugiyama M. (2011). "The Degrees of Freedom of Partial Least Squares Regression". Journal of the American Statistical Association 106 (494) https://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10107
Kraemer, N., Braun, M.L. (2007) "Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection", Proceedings of the 24th International Conference on Machine Learning, Omni Press, 441 - 448
Schwartz, G. (1979) "Estimating the Dimension of a Model" Annals of Statistics 26(5), 1651 - 1686.
See Also
Examples
## This is an internal function called by pls.ic